A255139 a(n) = n! - Fibonacci(n).
1, 0, 1, 4, 21, 115, 712, 5027, 40299, 362846, 3628745, 39916711, 479001456, 6227020567, 87178290823, 1307674367390, 20922789887013, 355687428094403, 6402373705725416, 121645100408827819, 2432902008176633235, 51090942171709429054
Offset: 0
Examples
For n = 0, a(0) = 0! - F(0) = 1 - 0 = 1.
Programs
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Maple
A255139 := proc(n) n!-combinat[fibonacci](n) ; end proc: # R. J. Mathar, Jul 08 2015
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Mathematica
Table[n! - Fibonacci[n], {n, 0, 20}] -
PARI
vector(30, n, n--; n! - fibonacci(n)) \\ Michel Marcus, Jul 05 2015
Formula
E.g.f.: 1/(1 - x) - 2*exp(x/2)*sinh(sqrt(5)*x/2)/sqrt(5). - Ilya Gutkovskiy, Dec 27 2016